{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"bbp_homoscedastic.ipynb","version":"0.3.2","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"accelerator":"GPU"},"cells":[{"cell_type":"code","metadata":{"id":"xAYPKSFrG8AF","colab_type":"code","outputId":"759c9aeb-2e17-4862-dc05-e3a724d437fa","executionInfo":{"status":"ok","timestamp":1557332409764,"user_tz":-60,"elapsed":15723,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":258}},"source":["!pip3 install http://download.pytorch.org/whl/cu92/torch-0.4.1-cp36-cp36m-linux_x86_64.whl\n","!pip3 install torchvision\n","!pip3 install GPy\n","import GPy\n","import time\n","import copy\n","import math\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import seaborn as sns\n","import torch\n","import torch.nn as nn\n","import torch.nn.functional as F\n","from torch.autograd import Variable\n","from torch.optim import Optimizer\n","\n","from torchvision import datasets, transforms\n","from torchvision.utils import make_grid\n","from tqdm import tqdm, trange\n","from google.colab import files\n","%config InlineBackend.figure_format = 'svg'"],"execution_count":51,"outputs":[{"output_type":"stream","text":["Requirement already satisfied: torch==0.4.1 from http://download.pytorch.org/whl/cu92/torch-0.4.1-cp36-cp36m-linux_x86_64.whl in /usr/local/lib/python3.6/dist-packages (0.4.1)\n","Requirement already satisfied: torchvision in /usr/local/lib/python3.6/dist-packages (0.2.2.post3)\n","Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from torchvision) (1.12.0)\n","Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from torchvision) (0.4.1)\n","Requirement already satisfied: pillow>=4.1.1 in /usr/local/lib/python3.6/dist-packages (from torchvision) (4.3.0)\n","Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from torchvision) (1.16.3)\n","Requirement already satisfied: olefile in /usr/local/lib/python3.6/dist-packages (from pillow>=4.1.1->torchvision) (0.46)\n","Requirement already satisfied: GPy in /usr/local/lib/python3.6/dist-packages (1.9.6)\n","Requirement already satisfied: paramz>=0.9.0 in /usr/local/lib/python3.6/dist-packages (from GPy) (0.9.4)\n","Requirement already satisfied: scipy>=0.16 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.2.1)\n","Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from GPy) (1.12.0)\n","Requirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.16.3)\n","Requirement already satisfied: decorator>=4.0.10 in /usr/local/lib/python3.6/dist-packages (from paramz>=0.9.0->GPy) (4.4.0)\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"1-7dNcVmHA3I","colab_type":"code","outputId":"ee895825-1c9c-4475-8455-ef100be3fd8b","executionInfo":{"status":"ok","timestamp":1557332409765,"user_tz":-60,"elapsed":15566,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["torch.cuda.device(0)\n","torch.cuda.get_device_name(torch.cuda.current_device())"],"execution_count":52,"outputs":[{"output_type":"execute_result","data":{"text/plain":["'Tesla K80'"]},"metadata":{"tags":[]},"execution_count":52}]},{"cell_type":"code","metadata":{"id":"_BzTB5WsP9Kx","colab_type":"code","colab":{}},"source":["def to_variable(var=(), cuda=True, volatile=False):\n","    out = []\n","    for v in var:\n","        \n","        if isinstance(v, np.ndarray):\n","            v = torch.from_numpy(v).type(torch.FloatTensor)\n","\n","        if not v.is_cuda and cuda:\n","            v = v.cuda()\n","\n","        if not isinstance(v, Variable):\n","            v = Variable(v, volatile=volatile)\n","\n","        out.append(v)\n","    return out"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Va8V78eFFsc9","colab_type":"code","colab":{}},"source":["def log_gaussian_loss(output, target, sigma, no_dim):\n","    exponent = -0.5*(target - output)**2/sigma**2\n","    log_coeff = -no_dim*torch.log(sigma)\n","    \n","    return - (log_coeff + exponent).sum()\n","\n","\n","def get_kl_divergence(weights, prior, varpost):\n","    prior_loglik = prior.loglik(weights)\n","    \n","    varpost_loglik = varpost.loglik(weights)\n","    varpost_lik = varpost_loglik.exp()\n","    \n","    return (varpost_lik*(varpost_loglik - prior_loglik)).sum()\n","\n","\n","class gaussian:\n","    def __init__(self, mu, sigma):\n","        self.mu = mu\n","        self.sigma = sigma\n","        \n","    def loglik(self, weights):\n","        exponent = -0.5*(weights - self.mu)**2/self.sigma**2\n","        log_coeff = -0.5*(np.log(2*np.pi) + 2*np.log(self.sigma))\n","        \n","        return (exponent + log_coeff).sum()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"colab_type":"code","id":"ASGi2Ecx5G-F","colab":{}},"source":["class BayesLinear_Normalq(nn.Module):\n","    def __init__(self, input_dim, output_dim, prior):\n","        super(BayesLinear_Normalq, self).__init__()\n","        self.input_dim = input_dim\n","        self.output_dim = output_dim\n","        self.prior = prior\n","        \n","        scale = (2/self.input_dim)**0.5\n","        rho_init = np.log(np.exp((2/self.input_dim)**0.5) - 1)\n","        self.weight_mus = nn.Parameter(torch.Tensor(self.input_dim, self.output_dim).uniform_(-0.05, 0.05))\n","        self.weight_rhos = nn.Parameter(torch.Tensor(self.input_dim, self.output_dim).uniform_(-2, -1))\n","        \n","        self.bias_mus = nn.Parameter(torch.Tensor(self.output_dim).uniform_(-0.05, 0.05))\n","        self.bias_rhos = nn.Parameter(torch.Tensor(self.output_dim).uniform_(-2, -1))\n","        \n","    def forward(self, x, sample = True):\n","        \n","        if sample:\n","            # sample gaussian noise for each weight and each bias\n","            weight_epsilons = Variable(self.weight_mus.data.new(self.weight_mus.size()).normal_())\n","            bias_epsilons =  Variable(self.bias_mus.data.new(self.bias_mus.size()).normal_())\n","            \n","            # calculate the weight and bias stds from the rho parameters\n","            weight_stds = torch.log(1 + torch.exp(self.weight_rhos))\n","            bias_stds = torch.log(1 + torch.exp(self.bias_rhos))\n","            \n","            # calculate samples from the posterior from the sampled noise and mus/stds\n","            weight_sample = self.weight_mus + weight_epsilons*weight_stds\n","            bias_sample = self.bias_mus + bias_epsilons*bias_stds\n","            \n","            output = torch.mm(x, weight_sample) + bias_sample\n","            \n","            # computing the KL loss term\n","            prior_cov, varpost_cov = self.prior.sigma**2, weight_stds**2\n","            KL_loss = 0.5*(torch.log(prior_cov/varpost_cov)).sum() - 0.5*weight_stds.numel()\n","            KL_loss = KL_loss + 0.5*(varpost_cov/prior_cov).sum()\n","            KL_loss = KL_loss + 0.5*((self.weight_mus - self.prior.mu)**2/prior_cov).sum()\n","            \n","            prior_cov, varpost_cov = self.prior.sigma**2, bias_stds**2\n","            KL_loss = KL_loss + 0.5*(torch.log(prior_cov/varpost_cov)).sum() - 0.5*bias_stds.numel()\n","            KL_loss = KL_loss + 0.5*(varpost_cov/prior_cov).sum()\n","            KL_loss = KL_loss + 0.5*((self.bias_mus - self.prior.mu)**2/prior_cov).sum()\n","            \n","            return output, KL_loss\n","        \n","        else:\n","            output = torch.mm(x, self.weight_mus) + self.bias_mus\n","            return output, KL_loss\n","        \n","    def sample_layer(self, no_samples):\n","        all_samples = []\n","        for i in range(no_samples):\n","            # sample gaussian noise for each weight and each bias\n","            weight_epsilons = Variable(self.weight_mus.data.new(self.weight_mus.size()).normal_())\n","            \n","            # calculate the weight and bias stds from the rho parameters\n","            weight_stds = torch.log(1 + torch.exp(self.weight_rhos))\n","            \n","            # calculate samples from the posterior from the sampled noise and mus/stds\n","            weight_sample = self.weight_mus + weight_epsilons*weight_stds\n","            \n","            all_samples += weight_sample.view(-1).cpu().data.numpy().tolist()\n","            \n","        return all_samples"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"colab_type":"code","id":"_8dV-QIq5G-I","colab":{}},"source":["class BBP_Homoscedastic_Model(nn.Module):\n","    def __init__(self, input_dim, output_dim, no_units, init_log_noise):\n","        super(BBP_Homoscedastic_Model, self).__init__()\n","        \n","        self.input_dim = input_dim\n","        self.output_dim = output_dim\n","        \n","        # network with two hidden and one output layer\n","        self.layer1 = BayesLinear_Normalq(input_dim, no_units, gaussian(0, 1))\n","        self.layer2 = BayesLinear_Normalq(no_units, output_dim, gaussian(0, 1))\n","        \n","        # activation to be used between hidden layers\n","        self.activation = nn.ReLU(inplace = True)\n","        self.log_noise = nn.Parameter(torch.cuda.FloatTensor([init_log_noise]))\n","\n","    \n","    def forward(self, x):\n","        \n","        KL_loss_total = 0\n","        x = x.view(-1, self.input_dim)\n","        \n","        x, KL_loss = self.layer1(x)\n","        KL_loss_total = KL_loss_total + KL_loss\n","        x = self.activation(x)\n","        \n","        x, KL_loss = self.layer2(x)\n","        KL_loss_total = KL_loss_total + KL_loss\n","        \n","        return x, KL_loss_total"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"colab_type":"code","id":"oAYelw3B5G-K","colab":{}},"source":["class BBP_Homoscedastic_Model_Wrapper:\n","    def __init__(self, input_dim, output_dim, no_units, learn_rate, batch_size, no_batches, init_log_noise):\n","        \n","        self.learn_rate = learn_rate\n","        self.batch_size = batch_size\n","        self.no_batches = no_batches\n","        \n","        self.network = BBP_Homoscedastic_Model(input_dim = input_dim, output_dim = output_dim,\n","                                               no_units = no_units, init_log_noise = init_log_noise)\n","        self.network.cuda()\n","        \n","        self.optimizer = torch.optim.SGD(self.network.parameters(), lr = self.learn_rate) \n","        # self.optimizer = torch.optim.Adam(self.network.parameters(), lr = self.learn_rate)\n","        self.loss_func = log_gaussian_loss\n","    \n","    def fit(self, x, y, no_samples):\n","        x, y = to_variable(var=(x, y), cuda=True)\n","        \n","        # reset gradient and total loss\n","        self.optimizer.zero_grad()\n","        fit_loss_total = 0\n","        \n","        for i in range(no_samples):\n","            output, KL_loss_total = self.network(x)\n","\n","            # calculate fit loss based on mean and standard deviation of output\n","            fit_loss_total = fit_loss_total + self.loss_func(output, y, self.network.log_noise.exp(), self.network.output_dim)\n","        \n","        KL_loss_total = KL_loss_total/self.no_batches\n","        total_loss = (fit_loss_total + KL_loss_total)/(no_samples*x.shape[0])\n","        total_loss.backward()\n","        self.optimizer.step()\n","\n","        return fit_loss_total/no_samples, KL_loss_total"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"ym6HBK-s8GnO","colab_type":"code","outputId":"d0b06fa7-3a28-405a-d0ec-34b04d8948c8","executionInfo":{"status":"ok","timestamp":1557332475991,"user_tz":-60,"elapsed":80768,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":374}},"source":["np.random.seed(2)\n","no_points = 400\n","lengthscale = 1\n","variance = 1.0\n","sig_noise = 0.3\n","x = np.random.uniform(-3, 3, no_points)[:, None]\n","x.sort(axis = 0)\n","\n","\n","k = GPy.kern.RBF(input_dim = 1, variance = variance, lengthscale = lengthscale)\n","C = k.K(x, x) + np.eye(no_points)*sig_noise**2\n","\n","y = np.random.multivariate_normal(np.zeros((no_points)), C)[:, None]\n","y = (y - y.mean())\n","x_train = x[75:325]\n","y_train = y[75:325]\n","\n","x_mean, x_std = x_train.mean(), x_train.var()**0.5\n","y_mean, y_std = y_train.mean(), y_train.var()**0.5\n","\n","x_train = (x_train - x_mean)/x_std\n","y_train = (y_train - y_mean)/y_std\n","\n","\n","num_epochs, batch_size, nb_train = 2000, len(x_train), len(x_train)\n","\n","net = BBP_Homoscedastic_Model_Wrapper(input_dim = 1, output_dim = 1, no_units = 100, learn_rate = 1e-1,\n","                                      batch_size = batch_size, no_batches = 1, init_log_noise = 0)\n","\n","fit_loss_train = np.zeros(num_epochs)\n","KL_loss_train = np.zeros(num_epochs)\n","total_loss = np.zeros(num_epochs)\n","\n","best_net, best_loss = None, float('inf')\n","\n","for i in range(num_epochs):\n","    \n","    fit_loss, KL_loss = net.fit(x_train, y_train, no_samples = 10)\n","    fit_loss_train[i] += fit_loss.cpu().data.numpy()\n","    KL_loss_train[i] += KL_loss.cpu().data.numpy()\n","    \n","    total_loss[i] = fit_loss_train[i] + KL_loss_train[i]\n","    \n","    if fit_loss < best_loss:\n","        best_loss = fit_loss\n","        best_net = copy.deepcopy(net.network)\n","        \n","    if i % 100 == 0 or i == num_epochs - 1:\n","        \n","        print(\"Epoch: %5d/%5d, Fit loss = %8.3f, KL loss = %8.3f, noise = %6.3f\" %\n","              (i + 1, num_epochs, fit_loss_train[i], KL_loss_train[i], net.network.log_noise.exp().cpu().data.numpy()))\n","\n","        samples = []\n","        for i in range(100):\n","            preds = net.network.forward(torch.linspace(-3, 3, 200).cuda())[0]\n","            samples.append(preds.cpu().data.numpy()[:, 0])"],"execution_count":58,"outputs":[{"output_type":"stream","text":["Epoch:     1/ 2000, Fit loss =  164.060, KL loss =  347.107, noise =  1.032\n","Epoch:   101/ 2000, Fit loss =   46.881, KL loss =  351.645, noise =  0.751\n","Epoch:   201/ 2000, Fit loss =   25.487, KL loss =  356.399, noise =  0.692\n","Epoch:   301/ 2000, Fit loss =    5.998, KL loss =  361.035, noise =  0.651\n","Epoch:   401/ 2000, Fit loss =   -1.786, KL loss =  365.240, noise =  0.598\n","Epoch:   501/ 2000, Fit loss =   -1.536, KL loss =  369.138, noise =  0.581\n","Epoch:   601/ 2000, Fit loss =  -26.350, KL loss =  373.013, noise =  0.555\n","Epoch:   701/ 2000, Fit loss =  -66.080, KL loss =  377.931, noise =  0.491\n","Epoch:   801/ 2000, Fit loss =  -82.541, KL loss =  384.716, noise =  0.441\n","Epoch:   901/ 2000, Fit loss = -115.861, KL loss =  390.306, noise =  0.425\n","Epoch:  1001/ 2000, Fit loss = -103.584, KL loss =  395.729, noise =  0.493\n","Epoch:  1101/ 2000, Fit loss = -143.469, KL loss =  400.659, noise =  0.396\n","Epoch:  1201/ 2000, Fit loss = -168.787, KL loss =  405.014, noise =  0.342\n","Epoch:  1301/ 2000, Fit loss =   63.918, KL loss =  408.421, noise =  0.427\n","Epoch:  1401/ 2000, Fit loss = -155.474, KL loss =  411.306, noise =  0.396\n","Epoch:  1501/ 2000, Fit loss = -107.294, KL loss =  413.371, noise =  0.531\n","Epoch:  1601/ 2000, Fit loss = -161.630, KL loss =  415.751, noise =  0.382\n","Epoch:  1701/ 2000, Fit loss =  -95.758, KL loss =  416.931, noise =  0.544\n","Epoch:  1801/ 2000, Fit loss =   97.973, KL loss =  418.029, noise =  1.095\n","Epoch:  1901/ 2000, Fit loss =  -81.332, KL loss =  419.733, noise =  0.603\n","Epoch:  2000/ 2000, Fit loss =  -89.126, KL loss =  420.687, noise =  0.582\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"D-I8x6HNO_2M","colab_type":"code","outputId":"f8b1e6ac-6a7a-4630-a2a1-0fb8bd8f50d5","executionInfo":{"status":"ok","timestamp":1557332480918,"user_tz":-60,"elapsed":85094,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":550}},"source":["samples = []\n","for i in range(100):\n","    preds = (best_net.forward(torch.linspace(-5, 5, 200).cuda())[0] * y_std) + y_mean\n","    samples.append(preds.cpu().data.numpy()[:, 0])\n","\n","samples = np.array(samples)\n","means = samples.mean(axis = 0)\n","\n","aleatoric = best_net.log_noise.exp().cpu().data.numpy()\n","epistemic = samples.var(axis = 0)**0.5\n","total_unc = (aleatoric**2 + epistemic**2)**0.5\n","\n","\n","c = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',\n","     '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']\n","\n","plt.figure(figsize = (6, 5))\n","plt.style.use('default')\n","plt.scatter((x_train * x_std) + x_mean, (y_train * y_std) + y_mean, s = 10, marker = 'x', color = 'black', alpha = 0.5)\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means + aleatoric, means + total_unc, color = c[0], alpha = 0.3, label = r'$\\sigma(y^*|x^*)$')\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means - total_unc, means - aleatoric, color = c[0], alpha = 0.3)\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means - aleatoric, means + aleatoric, color = c[1], alpha = 0.4, label = r'$\\EX[\\sigma^2]^{1/2}$')\n","plt.plot(np.linspace(-5, 5, 200)*x_std + x_mean, means, color = 'black', linewidth = 1)\n","plt.xlim([-5, 5])\n","plt.ylim([-5, 7])\n","plt.xlabel('$x$', fontsize=30)\n","plt.title('BBP', fontsize=40)\n","plt.tick_params(labelsize=30)\n","plt.xticks(np.arange(-4, 5, 2))\n","plt.gca().set_yticklabels([])\n","plt.gca().yaxis.grid(alpha=0.3)\n","plt.gca().xaxis.grid(alpha=0.3)\n","plt.savefig('bbp_homo.pdf', bbox_inches = 'tight')\n","\n","files.download(\"bbp_homo.pdf\")\n","\n","plt.show()"],"execution_count":59,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 600x500 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"397.0625pt\" version=\"1.1\" viewBox=\"0 0 356.2 397.0625\" width=\"356.2pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  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